This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A287594 #14 Feb 16 2025 08:33:46
%S A287594 3,4,12,28,72,184,480,1264,3360,8992,24192,65344,177024,480640,
%T A287594 1307136,3559168,9699840,26452480,72173568,196989952,537802752,
%U A287594 1468536832,4010582016,10954043392,29920862208,81733033984,223274237952,609947435008,1666309128192
%N A287594 Number of independent vertex sets in the n-helm graph.
%C A287594 Extended to a(0)-a(2) using the formula.
%H A287594 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HelmGraph.html">Helm Graph</a>
%H A287594 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H A287594 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, -2, -4).
%F A287594 a(n) = 2^n+A080040(n).
%F A287594 a(n) = 2^n+(1-sqrt(3))^n+(1+sqrt(3))^n.
%F A287594 a(n) = 4*a(n-1)-2*a(n-2)-4*a(n-3).
%F A287594 G.f.: (3-8*x+2*x^2)/((1-2*x)*(1-2*x-2*x^2)).
%t A287594 Table[2^n + (1 - Sqrt[3])^n + (1 + Sqrt[3])^n, {n, 0, 20}] // Expand
%t A287594 Table[2^n + 2^(n/2) LucasL[n, Sqrt[2]], {n, 0, 20}] // Round
%t A287594 LinearRecurrence[{4, -2, -4}, {4, 12, 28}, {0, 20}]
%t A287594 CoefficientList[Series[(3 - 8 x + 2 x^2)/(1 - 4 x + 2 x^2 + 4 x^3), {x, 0, 20}], x]
%Y A287594 Cf. A080040.
%K A287594 nonn,easy
%O A287594 0,1
%A A287594 _Eric W. Weisstein_, May 27 2017